## Wednesday, June 29, 2011

### The problem of measuring the price

In a liquid and transparent financial market, there is no doubt about the price. There is high pre-trade transparency, because orders are visible on the limit order book, and the best estimate of the true price is (bid+offer)/2. You glance at the screen and you know what is the price.

In a non-transparent market, it is hard to know the true price. Special schemes have to be constructed in order to measure the price. Price measurement does not happen for free' as a minor side effect of the very trading process.

### Why price measurement matters

As a thumb-rule, the best design for a derivatives contract is to use cash settlement, as long as you can be pretty certain about observing the price. If you can't measure the price, then physical settlement is better.

Cash settlement is a great technology. But it requires sound measurement of the price.

### Measuring price on an OTC market

In an OTC market, information is not visible at a glance. It is dispersed. Many traders have private information about the price, but you do not. If you could setup an electronic order book, you would see bid and offer at a glance: these are the prices at which a small buy and a small sell transaction could be done. On an OTC market, the dealer has a sense about where the market is, but you don't. So a natural strategy is that of asking the dealer what he is seeing.

Dealers have positions on the market, so we have to worry about what they say. Standard schemes used involve removing extreme observations, and thus coming up with a more robust price measure. These schemes have been used in India with the NSE MIBOR (the dominant price measure on the interest rate swaps market), the CMIE measurement of commodity spot prices for NCDEX, etc.

### RBI's measurement of the INR/USD exchange rate

In India, RBI is an information producer in reporting the INR/USD exchange rate at 12 noon. This official RBI price' is widely used in computing the settlement price for cash-settled derivatives on the rupee. It is used for the official closing price on the NSE currency futures/options market, which in many ways is shaping up as the main market where the INR exchange rate is discovered. As an example, yesterday (an expiration day), the open interest closed at $7.2 billion, and turnover was$6.2 billion.

RBI has not had a formal methodology for how this price is computed and reported.

I have always been a bit uncomfortable with RBI producing this vital information, since RBI has many other goals which can conflict with the goal of producing high quality information. But for a while, this seemed to be working.

### New methodology at RBI

On 1 July, their methodology will change to something new:

1. They will choose a random five-minute window from 10:30 to 12:30 (i.e. a two-hour window).
2. The reference rate will be computed using these five minutes.
3. It will be released at 13:00.

I cannot imagine the logic which led up to this, but I have to say that this is not a good idea.

A two hour window is a lot of time in the life of a market. The RBI reference rate is then no longer a reference rate of the market. It is a measure of the price at a randomly chosen time in that window. This makes it much less informative.

As an analogy, imagine if the official NSE closing price for Nifty was plucked out of a randomly chosen time from 2:30 PM to 3:30 PM. This would be a lot less informative as compared with the present methodology (value weighted average of all trades from 3 PM to 3:30 PM). It would be even better if NSE were to do a call auction from 3:15 PM to 3:30 PM and report that price as the official closing price. That would be sharp and interpretable.

All cash derivatives settling on the RBI reference rate will now suffer from a new source of uncertainty: the randomly chosen time at which the price is reported. The cash-and-carry arbitrageur needs to sell his spot position at the exact time at which the derivatives expire. In the case of the Nifty futures, there is a simple trading strategy which roughly approximates the Nifty closing price: In each of the last 30 minutes, do 1/30 of your required trade. This is typically automated, i.e. it requires algorithmic trading, but it's fully feasible.

With a randomly chosen timepoint over a two hour horizon, the arbitrageur does not know when to closeout. This will exert a negative impact on pricing efficiency and thus basis risk on the derivatives market.

If the INR/USD exchange rate is a random walk in trading time, then the 9% annualised volatility maps to a standard deviation of 28 basis points over a two hour horizon. On a base of Rs.45 a dollar, this is a standard deviation of 12.6 paisa. This is quite a bit for traders and arbitrageurs. These small issues have a disproportionate impact in contaminating market efficiency.

But wait. There are some people who know at what time the pricing is done: the banks who are polled! So suppose there is a fixed panel of banks who are asked by RBI. The moment the RBI phone call comes in, they closeout. These banks will find it profitable to do currency arbitrage while others are not. Such shifts in the currency arbitrage constitute a distortion induced by RBI's new method of price measurement.

### Lessons

RBI needs to cultivate improved knowledge of finance amidst its staff.

This illustrates the importance of legal process in rule-making. If RBI had gone through a formal notice-and-comment process, then they could have heard from external experts and desisted from doing this. I wasn't able to find a document on the RBI website explaining the rationale for what is being done.

Information production should be done by specialised information organisations. If information is produced by people who have other conflicting interests, then such sub-optimal decisions are more likely to arise.

Alternative information producers, such as Reuters, should leap into this opportunity by producing a better INR/USD reference rate. FEDAI already has an alternative reference rate. We should all switch away from the RBI reference rate towards alternatives.

Unfortunately, many people in the trade are fearful of the RBI and would not evaluate alternatives rationally. This tells us two things. First, RBI needs to be enveloped in the rule of law so that there is no fear of RBI on the part of market participants. Second, RBI should not be a producer of information. As long as two private agencies are producing INR/USD reference rates, the decision in the derivatives trade about what information measure to use will be based on technical merits alone. If someone then tries to come up with a scheme where a randomly chosen time over a two hour window is used for the measurement, his market share will go to zero.

Please note: LaTeX mathematics works. This means that if you want to say $10 you have to say \$10.